Studies Service page Degree Structure

Studies Service page advanced studies module - Mathematical Biology

This information is valid from academic year 2023-2024 onward. For prior requirements, please check the bottom of the page.

25-85 credits to be chosen from the following courses

- MAST30157 Case studies in Mathematics and statistics (5 cr)

- MAST30163 Mathematical modelling I (5cr)

- MAST30164 Mathematical modelling II (5 cr)

- LSI33006 Introduction to mathematical biology I (5 cr)

- LSI33007 Introduction to mathematical biology II (5 cr)

- MAST31505 Adaptive dynamics (10 cr)

- MAST30166 Stochastic population models I (5 cr)

- MAST30167 Stochastic population models II (5 cr)

- MAST31503 Spatial models in ecology and evolution (10 cr)

- LSI33002 Evolution and the theory of games I (5 cr)

- LSI33008 Evolution and the theory of games II (5 cr)

- LSI33003 Mathematics of infectious diseases (10 cr)

- MAST30156 Bifurcation theory (5 cr)

0-60 credits of other master courses in MAST;

0-25 credits of other master courses in TCM, LSI or Data Science;

0-35 credits in other sciences (or bachelor level courses agreed with your academic mentor);

5 credits from the Master's seminars I-II;

30 credits from the Master's thesis

Eva Kisdi

Eva Kisdi, Stefanus Geritz

**Aims of the studies**

We offer a science-based specialization especially suitable for research-oriented MSc students of applied mathematics and for all students interested in using mathematical models of real-life phenomena. We focus on biological applications, especially on ecology and evolution, because advanced modelling skills can be acquired through this field with little time needed to learn the specifics of the application area. To well-performing and motivated students, we offer publishable projects for the MSc thesis.

**Important to note**

(1) The courses of the Mathematical biology specialization are given every second year, so advanced planning is important. We maintain a strict schedule of our regular courses, so that students can plan their studies reliably:

Fall of odd years (e.g. fall 2023): Mathematical modelling I-II, Mathematics of infectious diseases

Fall of even years (e.g. fall 2024): Introduction to mathematical biology I-II, Evolution and the theory of games I-II

Spring of odd years (e.g. spring 2025): Stochastic population models I-II, Spatial models in ecology and evolution

Spring of even years (e.g. spring 2024): Adaptive dynamics

(2) Both the Mathematical modelling and the Introduction to mathematical biology courses serve as introductions to this specialization. We recommend these courses to all who are interested in modelling, also to students of other specializations. Parts I of these two courses overlap (no need to take Part I of both) but Parts II are different (you may want to take both).

(3) Some of our specialization courses have LSI codes but all are accepted as part of this specialization.

(4) We encourage learning numerical methods, acquiring basic skills in computer programming, and taking some courses in (bio)statistics during your MSc studies.

Additional courses (e.g. given by guest lecturers) that are not regularly taught are listed on this page.

**Prerequisites**

We expect a background in mathematics that enables learning mathematical concepts and techniques at a certain speed. For specific knowledge, we recommend BSc courses on differential equations, matrix algebra and probability. In more detail:

Differential equations: separable equations (with integration by parts), linear equations, systems of homogeneous linear equations.

Matrix algebra: products of matrices and vectors, rank, inverse, eigenvalue-eigenvector, diagonalisation.

Probability: calculating probabilities, independence, conditional probability, binomial, Poisson and exponential distributions, probability density function.

General guidance instructions and study plans

These study plans are **examples**. You can modify them as you wish, according to the requirements at the top of this page. The model study plans serve to show how you can accommodate many of the specialization courses but the requirement is only 20 credits from these.

**Time schedule if starting in an odd year **(e.g. autumn 2023)

**Year 1, autumn** (32 cr):

Mathematical modelling I-II (10 cr)

Mathematics of infectious diseases (10 cr)

Functional analysis (10 cr) OR statistics courses

Master's seminar I (2 cr)

**Year 1, spring **(30 cr):

Adaptive dynamics (10 cr)

Bifurcation theory (independent project, 5cr)

Introduction to programming (5 cr, period III) + Advanced course in programming (5 cr, period IV)

optional studies (5cr)

**Year 2, autumn **(28 cr):

Introduction to mathematical biology II (5cr)

Evolution and the theory of games I-II (10cr)

Master's seminar II (3cr)

thesis work (of 10cr)

**Year 2, spring **(30 cr):

Stochastic population models I-II OR Spatial models in ecology and evolution (10 cr)

thesis work (of 20 cr)

**Time schedule if the student starts in an even year** (e.g. autumn 2024)

**Year 1, autumn **(32 cr):

Introduction to mathematical biology I-II (10 cr)

Evolution and the theory of games I-II (10 cr)

Functional analysis (10 cr) OR statistics courses

Master's seminar I (2 cr)

**Year 1, spring **(30 op):

Stochastic population models I-II (10cr)

Spatial models in ecology and evolution (10 op)

Introduction to programming (5 cr) + Advanced course in programming (5 cr)

**Year 2, autumn** (28 op):

Mathematics of infectious diseases (10 op)

Bifurcation theory (independent project, 5cr)

Master's seminar II (3 cr)

thesis work (of 10 cr)

**Year 2, spring** (30 cr):

Adaptive dynamics (10 cr)

thesis work (of 20 cr)

Prior to curriculum 2023-26, this specialization was called Mathematical modelling. Students enrolled before the fall of 2023 can complete this specialization according to the following requirements:

Mandatory core courses, 10 cr

MAST31501 Mathematical modelling (10 cr) OR LSI33006 Introduction to mathematical biology I (5 cr) and LSI33007 Introduction to mathematical biology II (5 cr)

Specialization courses, at least 15 cr from this list:

MAST31505 Adaptive dynamics (10 cr)

LSI33002 Evolution and the theory of games I (5 cr)

LSI33008 Evolution and the theory of games II (5 cr)

LSI33003 Mathematics of infectious diseases (10 cr)

MAST31503 Spatial models in ecology and evolution (10 cr)

MAST30166 Stochastic population models I (5 cr)

MAST30167 Stochastic population models II (5 cr)

MAST30001 Master´s thesis seminar (5 cr)

MAST31000 Master´s thesis (30 cr) (the link includes grading scale and criteria)

Other advanced courses from the list of core courses, mathematics, applied mathematics, statistics courses and/or courses from other programmes as approved in personal study plan.